Modular square roots. More...

#include <givintsqrootmod.h>

Inheritance diagram for IntSqrtModDom< RandIter >:

Collaboration diagram for IntSqrtModDom< RandIter >:

Public Types
typedef IntFactorDom< RandIter >	Father_t
typedef IntFactorDom< RandIter > ::Rep	Rep
typedef RandIter	random_generator
typedef Rep	Element

Public Member Functions
	IntSqrtModDom (RandIter g=RandIter())
Rep &	sqrootmod (Rep &x, const Rep &a, const Rep &n) const
Rep &	sqrootmodprime (Rep &x, const Rep &a, const Rep &p) const
Rep &	sqrootmodprimepower (Rep &x, const Rep &a, const Rep &p, const unsigned long k, const Rep &pk) const
Rep &	sqrootmodpoweroftwo (Rep &x, const Rep &a, const unsigned long k, const Rep &pk) const
Rep &	factor (Rep &r, const Rep &n, unsigned long loops=0) const
Rep &	iffactorprime (Rep &r, const Rep &n, unsigned long loops=0) const
Rep &	primefactor (Rep &r, const Rep &n) const
template<class Container1 , class Container2 >
bool	set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
	Factors with primes.
template<class Container >
void	set (Container &, const Rep &) const
template<class Container >
void	Erathostene (Container &, const Rep &) const
Rep &	Erathostene (Rep &, const Rep &p) const
	returns a small factor
template<class Container , class Cont2 , class Cont3 >
Container &	divisors (Container &L, const Cont2 &Lf, const Cont3 &Le) const
template<class Container >
Container &	divisors (Container &, const Rep &) const
Rep &	Pollard (const RandIter &, Rep &, const Rep &n, unsigned long threshold=0) const
Rep &	Lenstra (const RandIter &, Rep &, const Rep &n, const Rep &B1=10000000, const unsigned long curves=30) const
std::ostream &	write (std::ostream &o, const Rep &n) const
template<class Array >
std::ostream &	write (std::ostream &o, Array &, const Rep &n) const
std::ostream &	write (std::ostream &o) const
std::ostream &	write (std::ostream &o, const Rep &n) const
int	isprime (const Rep &n, int r=5) const
unsigned int	isprimepower (Rep &, const Rep &) const
template<class RandIter >
unsigned int	Miller (RandIter &g, const Rep &n=5) const
template<class RandIter >
Rep &	test_Lehmann (RandIter &g, Rep &, const Rep &n=5) const
template<class RandIter >
int	Lehmann (RandIter &g, const Rep &n=5) const
int	isprime_Tabule (const int n) const
int	isprime_Tabule2 (const int n) const
Rep &	nextprime (Rep &, const Rep &, int r=5) const
Rep &	prevprime (Rep &, const Rep &, int r=5) const
Rep &	nextprimein (Rep &, int r=5) const
Rep &	prevprimein (Rep &, int r=5) const
int	local_prime (const Rep &n, int r=5) const
int	operator== (const IntegerDom &) const
int	operator!= (const IntegerDom &) const
Rep &	init (Rep &a) const
Rep &	init (Rep &a, const Rep &b) const
Rep &	read (Rep &a, const long i) const
Rep &	read (Rep &a, const unsigned long i) const
Rep &	read (Rep &a, const int i) const
Rep &	read (Rep &a, const unsigned int i) const
std::istream &	read (std::istream &i)
std::istream &	read (std::istream &i, Rep &n) const
Rep &	convert (Rep &a, const Rep &b) const
template<class XXX >
XXX &	convert (XXX &x, const Rep &a) const
Rep &	assign (Rep &a, const Rep &b) const
const Rep &	access (const Rep &a) const
Rep &	mul (Rep &r, const Rep &a, const Rep &b) const
Rep &	div (Rep &r, const Rep &a, const Rep &b) const
Rep &	mod (Rep &r, const Rep &a, const Rep &b) const
Rep &	add (Rep &r, const Rep &a, const Rep &b) const
Rep &	sub (Rep &r, const Rep &a, const Rep &b) const
Rep &	divmod (Rep &q, Rep &r, const Rep &a, const Rep &b) const
Rep &	divexact (Rep &q, const Rep &a, const Rep &b) const
Rep &	mulin (Rep &r, const Rep &a) const
Rep &	divin (Rep &r, const Rep &a) const
Rep &	modin (Rep &r, const Rep &a) const
Rep &	addin (Rep &r, const Rep &a) const
Rep &	subin (Rep &r, const Rep &a) const
Rep &	axpy (Rep &r, const Rep &a, const Rep &b, const Rep &c) const
Rep &	maxpy (Rep &r, const Rep &a, const Rep &b, const Rep &c) const
Rep &	maxpyin (Rep &r, const Rep &a, const Rep &b) const
Rep &	axmy (Rep &r, const Rep &a, const Rep &b, const Rep &c) const
Rep &	axpyin (Rep &r, const Rep &a, const Rep &b) const
Rep &	axmyin (Rep &r, const Rep &a, const Rep &b) const
Rep &	neg (Rep &r, const Rep &a) const
Rep &	negin (Rep &r) const
Rep &	gcd (Rep &g, Rep &u, Rep &v, const Rep &a, const Rep &b) const
Rep &	gcd (Rep &g, const Rep &a, const Rep &b) const
Rep &	lcm (Rep &l, const Rep &a, const Rep &b) const
Rep &	lcmin (Rep &l, const Rep &a) const
Rep &	inv (Rep &u, const Rep &a, const Rep &b) const
Rep &	invin (Rep &u, const Rep &b) const
Rep &	pow (Rep &r, const Rep &n, const long l) const
Rep &	pow (Rep &r, const Rep &n, const unsigned long l) const
Rep &	pow (Rep &r, const Rep &n, const int l) const
Rep &	pow (Rep &r, const Rep &n, const unsigned int l) const
Rep &	sqrt (Rep &s, const Rep &n) const
Rep &	sqrt (Rep &s, Rep &r, const Rep &n) const
long	logp (const Rep &a, const Rep &p) const
Rep &	powmod (Rep &r, const Rep &n, const long e, const Rep &m) const
Rep &	powmod (Rep &r, const Rep &n, const Rep &e, const Rep &m) const
unsigned long	length (const Rep &a) const
int	sign (const Rep &a) const
bool	isZero (const Rep &a) const
bool	isOne (const Rep &a) const
bool	areEqual (const Rep &a, const Rep &b) const
bool	areNEqual (const Rep &a, const Rep &b) const
bool	isgeq (const Rep &a, const Rep &b) const
bool	isgeq (const long b, const Rep &a) const
bool	isgeq (const Rep &a, const long b) const
bool	isleq (const Rep &a, const Rep &b) const
bool	isleq (const long b, const Rep &a) const
bool	isleq (const Rep &a, const long b) const
bool	isgt (const Rep &a, const Rep &b) const
bool	isgt (const long b, const Rep &a) const
bool	isgt (const Rep &a, const long b) const
bool	islt (const Rep &a, const Rep &b) const
bool	islt (const long b, const Rep &a) const
bool	islt (const Rep &a, const long b) const
template<class RandIter >
Rep &	random (RandIter &, Rep &r, long s=1) const
template<class RandIter >
Rep &	random (RandIter &, Rep &r, const Rep &b) const
template<class RandIter >
Rep &	nonzerorandom (RandIter &, Rep &r, long s=1) const
template<class RandIter >
Rep &	nonzerorandom (RandIter &, Rep &r, const Rep &b) const

Data Fields
const Integer	one
const Integer	mOne
const Integer	zero

Protected Member Functions
Rep &	sqrootlinear (Rep &x, const Rep &a, const Rep &p, const unsigned long k) const
Rep &	sqroottwolinear (Rep &x, const Rep &a, const unsigned long k) const
Rep &	sqroothensellift (Rep &x, const Rep &a, const Rep &p, const unsigned long k, const Rep &pk) const
Rep &	sqrootonemorelift (Rep &x, const Rep &a, const Rep &p, const unsigned long k, const Rep &pk) const
Rep &	sqrootmodtwolift (Rep &x, const Rep &a, const unsigned long k, const Rep &pk) const

Protected Attributes
RandIter	_g

Detailed Description

template<class RandIter = GivRandom>
class Givaro::IntSqrtModDom< RandIter >

Modular square roots.

Examples:: examples/Integer/ModularSquareRoot.C.

Member Typedef Documentation

typedef IntFactorDom< RandIter > Father_t

typedef IntFactorDom< RandIter >::Rep Rep

Reimplemented from IntegerDom.

typedef RandIter random_generator

inherited

Reimplemented in IntRSADom< RandIter >.

typedef Rep Element

inherited

Reimplemented in IntRSADom< RandIter >, and Poly1PadicDom< Domain, Dense >.

Examples:: examples/Integer/lambda.C, examples/Integer/lambda_inv.C, examples/Integer/phi.C, examples/Integer/primitiveelement.C, examples/Integer/primitiveroot.C, and examples/Integer/probable_primroot.C.

Constructor & Destructor Documentation

IntSqrtModDom ( RandIter g = RandIter () )

inline

Member Function Documentation

Rep& sqrootmod	(	Rep &	x,
		const Rep &	a,
		const Rep &	n
	)		const

inline

IntSqrtModDom< RandIter >::Rep & sqrootmodprime	(	Rep &	x,
		const Rep &	a,
		const Rep &	p
	)		const

inline

IntSqrtModDom< RandIter >::Rep & sqrootmodprimepower	(	Rep &	x,
		const Rep &	a,
		const Rep &	p,
		const unsigned long	k,
		const Rep &	pk
	)		const

inline

IntSqrtModDom< RandIter >::Rep & sqrootmodpoweroftwo	(	Rep &	x,
		const Rep &	a,
		const unsigned long	k,
		const Rep &	pk
	)		const

inline

IntSqrtModDom< RandIter >::Rep & sqrootlinear	(	Rep &	x,
		const Rep &	a,
		const Rep &	p,
		const unsigned long	k
	)		const

inlineprotected

IntSqrtModDom< RandIter >::Rep & sqroottwolinear	(	Rep &	x,
		const Rep &	a,
		const unsigned long	k
	)		const

inlineprotected

IntSqrtModDom< RandIter >::Rep & sqroothensellift	(	Rep &	x,
		const Rep &	a,
		const Rep &	p,
		const unsigned long	k,
		const Rep &	pk
	)		const

inlineprotected

IntSqrtModDom< RandIter >::Rep & sqrootonemorelift	(	Rep &	x,
		const Rep &	a,
		const Rep &	p,
		const unsigned long	k,
		const Rep &	pk
	)		const

inlineprotected

IntSqrtModDom< RandIter >::Rep & sqrootmodtwolift	(	Rep &	x,
		const Rep &	a,
		const unsigned long	k,
		const Rep &	pk
	)		const

inlineprotected

Rep& factor	(	Rep &	r,
		const Rep &	n,
		unsigned long	loops = `0`
	)		const

inlineinherited

Rep& iffactorprime	(	Rep &	r,
		const Rep &	n,
		unsigned long	loops = `0`
	)		const

inlineinherited

Rep& primefactor	(	Rep &	r,
		const Rep &	n
	)		const

inlineinherited

bool set	(	Container1 &	setint,
		Container2 &	setpwd,
		const Rep &	a,
		unsigned long	loops = `0`
	)		const

inherited

Factors with primes.

void set	(	Container &	Lf,
		const Rep &	n
	)		const

inherited

void Erathostene	(	Container &	Lf,
		const Rep &	p
	)		const

inherited

Rep& Erathostene	(	Rep &	,
		const Rep &	p
	)		const

inherited

returns a small factor

Container & divisors	(	Container &	L,
		const Cont2 &	Lf,
		const Cont3 &	Le
	)		const

inherited

Container & divisors	(	Container &	L,
		const Rep &	n
	)		const

inherited

IntFactorDom< RandIter >::Rep & Pollard	(	const RandIter &	gen,
		Rep &	g,
		const Rep &	n,
		unsigned long	threshold = `0`
	)		const

inherited

IntFactorDom< RandIter >::Rep & Lenstra	(	const RandIter &	gen,
		Rep &	g,
		const Rep &	n,
		const Rep &	B1 = `10000000`,
		const unsigned long	curves = `30`
	)		const

inherited

std::ostream & write	(	std::ostream &	o,
		const Rep &	n
	)		const

inherited

std::ostream & write	(	std::ostream &	o,
		Array &	Lf,
		const Rep &	n
	)		const

inherited

std::ostream& write ( std::ostream & o ) const

inlineinherited

Examples:: examples/Integer/lambda.C, examples/Integer/lambda_inv.C, examples/Integer/phi.C, examples/Integer/primitiveelement.C, and examples/Integer/probable_primroot.C.

std::ostream& write	(	std::ostream &	o,
		const Rep &	n
	)		const

inlineinherited

int isprime	(	const Rep &	n,
		int	r = `5`
	)		const

inlineinherited

Examples:: examples/Integer/isprime.C, examples/Integer/nb_primes.C, and examples/Integer/ProbLucas.C.

unsigned int isprimepower	(	Rep &	q,
		const Rep &	u
	)		const

inherited

Examples:: examples/Integer/ispower.C.

unsigned int Miller	(	RandIter &	g,
		const Rep &	n = `5`
	)		const

inherited

IntPrimeDom::Rep & test_Lehmann	(	RandIter &	g,
		Rep &	r,
		const Rep &	n = `5`
	)		const

inherited

int Lehmann	(	RandIter &	g,
		const Rep &	n = `5`
	)		const

inherited

int isprime_Tabule ( const int n ) const

inherited

int isprime_Tabule2 ( const int n ) const

inherited

IntPrimeDom::Rep & nextprime	(	Rep &	n,
		const Rep &	p,
		int	r = `5`
	)		const

inherited

IntPrimeDom::Rep & prevprime	(	Rep &	n,
		const Rep &	p,
		int	r = `5`
	)		const

inherited

IntPrimeDom::Rep & nextprimein	(	Rep &	n,
		int	r = `5`
	)		const

inherited

Examples:: examples/Integer/nb_primes.C, examples/Integer/nextprime.C, and examples/Polynomial/PolynomialCRT.C.

IntPrimeDom::Rep & prevprimein	(	Rep &	n,
		int	r = `5`
	)		const

inherited

Examples:: examples/Integer/prevprime.C.

int local_prime	(	const Rep &	n,
		int	r = `5`
	)		const

inlineinherited

int operator== ( const IntegerDom & ) const

inlineinherited

int operator!= ( const IntegerDom & ) const

inlineinherited

Rep& init ( Rep & a ) const

inlineinherited

Rep& init	(	Rep &	a,
		const Rep &	b
	)		const

inlineinherited

Rep& read	(	Rep &	a,
		const long	i
	)		const

inlineinherited

Rep& read	(	Rep &	a,
		const unsigned long	i
	)		const

inlineinherited

Rep& read	(	Rep &	a,
		const int	i
	)		const

inlineinherited

Rep& read	(	Rep &	a,
		const unsigned int	i
	)		const

inlineinherited

std::istream& read ( std::istream & i )

inlineinherited

std::istream& read	(	std::istream &	i,
		Rep &	n
	)		const

inlineinherited

Rep& convert	(	Rep &	a,
		const Rep &	b
	)		const

inlineinherited

XXX& convert	(	XXX &	x,
		const Rep &	a
	)		const

inlineinherited

Rep& assign	(	Rep &	a,
		const Rep &	b
	)		const

inlineinherited

const Rep& access ( const Rep & a ) const

inlineinherited

Rep& mul	(	Rep &	r,
		const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

Examples:: examples/Integer/ilcm.C.

Rep& div	(	Rep &	r,
		const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

Rep& mod	(	Rep &	r,
		const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

Rep& add	(	Rep &	r,
		const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

Rep& sub	(	Rep &	r,
		const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

Examples:: examples/Integer/ProbLucas.C.

Rep& divmod	(	Rep &	q,
		Rep &	r,
		const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

Rep& divexact	(	Rep &	q,
		const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

Rep& mulin	(	Rep &	r,
		const Rep &	a
	)		const

inlineinherited

Examples:: examples/Integer/ilcm.C, and examples/Integer/ProbLucas.C.

Rep& divin	(	Rep &	r,
		const Rep &	a
	)		const

inlineinherited

Examples:: examples/Integer/ilcm.C.

Rep& modin	(	Rep &	r,
		const Rep &	a
	)		const

inlineinherited

Examples:: examples/Integer/ProbLucas.C.

Rep& addin	(	Rep &	r,
		const Rep &	a
	)		const

inlineinherited

Examples:: examples/Integer/ProbLucas.C.

Rep& subin	(	Rep &	r,
		const Rep &	a
	)		const

inlineinherited

Rep& axpy	(	Rep &	r,
		const Rep &	a,
		const Rep &	b,
		const Rep &	c
	)		const

inlineinherited

Rep& maxpy	(	Rep &	r,
		const Rep &	a,
		const Rep &	b,
		const Rep &	c
	)		const

inlineinherited

Rep& maxpyin	(	Rep &	r,
		const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

Rep& axmy	(	Rep &	r,
		const Rep &	a,
		const Rep &	b,
		const Rep &	c
	)		const

inlineinherited

Rep& axpyin	(	Rep &	r,
		const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

Rep& axmyin	(	Rep &	r,
		const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

Rep& neg	(	Rep &	r,
		const Rep &	a
	)		const

inlineinherited

Rep& negin ( Rep & r ) const

inlineinherited

Rep& gcd	(	Rep &	g,
		Rep &	u,
		Rep &	v,
		const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

Examples:: examples/Integer/igcd.C, examples/Integer/igcdext.C, examples/Integer/ilcm.C, and examples/Integer/ProbLucas.C.

Rep& gcd	(	Rep &	g,
		const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

Rep& lcm	(	Rep &	l,
		const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

Examples:: examples/Integer/ilcm.C.

Rep& lcmin	(	Rep &	l,
		const Rep &	a
	)		const

inlineinherited

Examples:: examples/Integer/ilcm.C.

Rep& inv	(	Rep &	u,
		const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

Rep& invin	(	Rep &	u,
		const Rep &	b
	)		const

inlineinherited

Rep& pow	(	Rep &	r,
		const Rep &	n,
		const long	l
	)		const

inlineinherited

Rep& pow	(	Rep &	r,
		const Rep &	n,
		const unsigned long	l
	)		const

inlineinherited

Rep& pow	(	Rep &	r,
		const Rep &	n,
		const int	l
	)		const

inlineinherited

Rep& pow	(	Rep &	r,
		const Rep &	n,
		const unsigned int	l
	)		const

inlineinherited

Rep& sqrt	(	Rep &	s,
		const Rep &	n
	)		const

inlineinherited

Rep& sqrt	(	Rep &	s,
		Rep &	r,
		const Rep &	n
	)		const

inlineinherited

long logp	(	const Rep &	a,
		const Rep &	p
	)		const

inlineinherited

Rep& powmod	(	Rep &	r,
		const Rep &	n,
		const long	e,
		const Rep &	m
	)		const

inlineinherited

Examples:: examples/Integer/ProbLucas.C.

Rep& powmod	(	Rep &	r,
		const Rep &	n,
		const Rep &	e,
		const Rep &	m
	)		const

inlineinherited

unsigned long length ( const Rep & a ) const

inlineinherited

int sign ( const Rep & a ) const

inlineinherited

bool isZero ( const Rep & a ) const

inlineinherited

bool isOne ( const Rep & a ) const

inlineinherited

bool areEqual	(	const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

bool areNEqual	(	const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

bool isgeq	(	const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

bool isgeq	(	const long	b,
		const Rep &	a
	)		const

inlineinherited

bool isgeq	(	const Rep &	a,
		const long	b
	)		const

inlineinherited

bool isleq	(	const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

bool isleq	(	const long	b,
		const Rep &	a
	)		const

inlineinherited

bool isleq	(	const Rep &	a,
		const long	b
	)		const

inlineinherited

bool isgt	(	const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

bool isgt	(	const long	b,
		const Rep &	a
	)		const

inlineinherited

bool isgt	(	const Rep &	a,
		const long	b
	)		const

inlineinherited

bool islt	(	const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

bool islt	(	const long	b,
		const Rep &	a
	)		const

inlineinherited

bool islt	(	const Rep &	a,
		const long	b
	)		const

inlineinherited

Rep& random	(	RandIter &	,
		Rep &	r,
		long	s = `1`
	)		const

inlineinherited

Examples:: examples/Integer/ProbLucas.C.

Rep& random	(	RandIter &	,
		Rep &	r,
		const Rep &	b
	)		const

inlineinherited

Rep& nonzerorandom	(	RandIter &	,
		Rep &	r,
		long	s = `1`
	)		const

inlineinherited

Rep& nonzerorandom	(	RandIter &	,
		Rep &	r,
		const Rep &	b
	)		const

inlineinherited

Field Documentation

RandIter _g

protectedinherited

const Integer one

inherited

const Integer mOne

inherited

const Integer zero

inherited

The documentation for this class was generated from the following files:

Public Types

Public Member Functions

Data Fields

Protected Member Functions

Protected Attributes

Detailed Description

template<class RandIter = GivRandom> class Givaro::IntSqrtModDom< RandIter >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Field Documentation

template<class RandIter = GivRandom>
class Givaro::IntSqrtModDom< RandIter >